diff --git a/imperative/src/impl/interpreter/commands.h b/imperative/src/impl/interpreter/commands.h
index e3c632058fb1fe5b1984652379275e527f620754..ed38e3e90c1a26b448c21b0247fa4dbb00a5d261 100644
--- a/imperative/src/impl/interpreter/commands.h
+++ b/imperative/src/impl/interpreter/commands.h
@@ -213,7 +213,7 @@ using IdentifiedCommand = std::pair<uint64_t, Command>;
 template <>
 struct ToStringTrait<interpreter::intl::Command>{
     std::string operator()(const interpreter::intl::Command& cmd) const {
-        return std::visit([](auto& cmd){
+        return std::visit([](const auto& cmd){
             std::string result = cmd.get_name();
             result += "{";
             cmd.get_props([&](const char* key, auto&& value) {
diff --git a/imperative/src/impl/interpreter/interpreter_impl.cpp b/imperative/src/impl/interpreter/interpreter_impl.cpp
index f6158498f296734abf0c7c43c7ae7ada5331d862..4430c2fcfdaf701030ffe68f0dafe4fa68e6d0bb 100644
--- a/imperative/src/impl/interpreter/interpreter_impl.cpp
+++ b/imperative/src/impl/interpreter/interpreter_impl.cpp
@@ -481,8 +481,8 @@ void ChannelImpl::process_one_task(IdentifiedCommand& icmd) {
         finished = true;
     };
     //TODO: remove std::visit for support osx 10.12
-    auto cmd_visitor = [&](auto& cmd) {
-            using T = std::remove_reference_t<decltype(cmd)>;
+    auto cmd_visitor = [&](const auto& cmd) {
+            using T = std::decay_t<decltype(cmd)>;
             if constexpr (std::is_same_v<T, Put>) {
                 auto value = cmd.no_cache ? std::make_shared<Tensor>(cmd.value) : Tensor::make(cmd.value);
                 produce_tensor(cmd.dest, std::move(value));
@@ -598,10 +598,10 @@ void ChannelImpl::process_one_task(IdentifiedCommand& icmd) {
                 do_finish_command();
                 m_worker_state.profiler->record_host<WorkerEndScope>(cmd.scope_name);
             } else {
-                static_assert(std::is_same_v<T, T>);
+                static_assert(!std::is_same_v<T, T>);
             }
     };
-    std::visit([&](auto& cmd){
+    std::visit([&](const auto& cmd){
         using T = std::decay_t<decltype(cmd)>;
         if (!m_worker_state.options.catch_worker_execption) {
             cmd_visitor(cmd);
diff --git a/imperative/src/impl/interpreter/profiler.cpp b/imperative/src/impl/interpreter/profiler.cpp
index 7517b4858d865c8c03b27e3f4b5287a0c33d86be..5d294aecae97c40de26f5ebe6755d0ba626ddedf 100644
--- a/imperative/src/impl/interpreter/profiler.cpp
+++ b/imperative/src/impl/interpreter/profiler.cpp
@@ -97,7 +97,7 @@ struct InterpreterProfilerDumpChromeTimelineContext {
     };
 
     // convert Command to json object. Has to be an callable object
-    static auto constexpr cmd_to_args = [](auto&& cmd) {
+    static auto constexpr cmd_to_args = [](const auto& cmd) {
         auto args = json::Object::make();
         cmd.get_props([&](const char* key, auto&& value){
             (*args)[key] = json::String::make(to_string(value));
@@ -108,14 +108,14 @@ struct InterpreterProfilerDumpChromeTimelineContext {
 
     void process() {
         // enumerate and process each record
-        for (auto&& record: profile_data.records) {
-            std::visit([this](auto& record){
+        for (auto& record: profile_data.records) {
+            std::visit([this](const auto& record){
                 using TEvent = std::decay_t<decltype(record.data)>;
                 Session<TEvent>(*this, record).process();
             }, record);
         }
         for (size_t tid = 0; tid < thread_list.size(); ++tid) {
-            auto tname = std::visit([&](auto& host_or_device) -> std::string{
+            auto tname = std::visit([&](auto host_or_device) -> std::string{
                 using T = std::decay_t<decltype(host_or_device)>;
                 if constexpr (std::is_same_v<T, std::thread::id>) {
                     // take name from host_map
@@ -142,11 +142,11 @@ struct InterpreterProfilerDumpChromeTimelineContext {
     template <typename TEvent>
     struct Session {
         InterpreterProfilerDumpChromeTimelineContext& ctx;
-        ProfilerBase::EventRecord<TEvent>& record;
-        TEvent& data;
+        const ProfilerBase::EventRecord<TEvent>& record;
+        const TEvent& data;
 
         Session(InterpreterProfilerDumpChromeTimelineContext& ctx,
-                ProfilerBase::EventRecord<TEvent>& record)
+                const ProfilerBase::EventRecord<TEvent>& record)
             : ctx{ctx}, record{record}, data{record.data} {}
 
         uint64_t get_host_tid() {
diff --git a/imperative/src/include/megbrain/imperative/profiler.h b/imperative/src/include/megbrain/imperative/profiler.h
index e687bea2d3b2f8800add80f39602e79171c0e58f..702befabf3763287dec10a56b5d2e52678983369 100644
--- a/imperative/src/include/megbrain/imperative/profiler.h
+++ b/imperative/src/include/megbrain/imperative/profiler.h
@@ -57,7 +57,7 @@ public:
         Host tid;
         double time;
 
-        void wait() {}
+        void wait() const {}
     };
 
     struct DeviceInstant {
@@ -65,7 +65,7 @@ public:
         std::shared_ptr<CompNode::Event> event;
         double after;
 
-        void wait() {
+        void wait() const {
             event->host_wait();
         }
     };
@@ -77,16 +77,16 @@ public:
         Instant instant;
         TEvent data;
 
-        HostInstant& host() {
+        const HostInstant& host() const {
             return std::get<HostInstant>(instant);
         }
 
-        DeviceInstant device() {
+        const DeviceInstant& device() const {
             return std::get<DeviceInstant>(instant);
         }
 
-        void wait() {
-            std::visit([&](auto& instant){ instant.wait(); }, instant);
+        void wait() const {
+            std::visit([&](const auto& instant){ instant.wait(); }, instant);
         }
     };
 protected:
@@ -173,7 +173,7 @@ public:
         mgb_assert(m_status == Profiling, "profiler not active");
         m_status = Stopped;
         for (auto&& record: m_record_list) {
-            std::visit([&](auto& record){
+            std::visit([&](const auto& record){
                 record.wait();
             }, record);
         }
@@ -312,7 +312,7 @@ public:
         return m_content.back();
     }
 
-    std::shared_ptr<json::Array> to_json() {
+    std::shared_ptr<json::Array> to_json() const {
         auto result = json::Array::make();
         for (auto&& event: m_content) {
             result->add(event.to_json());